A general Liouville type theorem for some conformally invariant fully nonlinear equations
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چکیده
Various Liouville type theorems for conformally invariant equations have been obtained by Obata ([9]), Gidas, Ni and Nirenberg ([4]), Caffarelli, Gidas and Spruck ([1]), Viaclovsky ([10] and [11]), Chang, Gursky and Yang ([2] and [3]), and Li and Li ([5], [6] and [7]). See e. g. theorem 1.3 and remark 1.6 in [6] where these results (except for the one in [7]) are stated more precisely. In this paper we give a general Liouville type theorem for conformally invariant fully nonlinear equations. This extends the above mentioned Liouville type theorems. For n ≥ 3, let S be the set of n×n real symmetric matrices, S + ⊂ S n×n be the set of positive definite matrices, and let O(n) be the set of n×n real orthogonal matrices. For a positive C function u, let
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تاریخ انتشار 2003